If $$A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]$$, then $$A A^T$$ is a

If $$A X=D$$ represents the system of simultaneous linear equations $$x+y+z=6, 5 x-y+2 z=3$$ and $$2 x+y-z=-5$$, then (Adj $$A$$) $$D=$$

If $$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right]$$, then $$\operatorname{det}\left(A^6+B^6\right)=$$

Let $$G(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$$. If $$x+y=0$$ then $$G(x) G(y)=$$